Background When an outcome of interest in a clinical trial is late-occurring or difficult to obtain, surrogate markers can extract information about the effect of the treatment on the outcome of interest. Understanding associations between the causal effect (CE) of treatment on the outcome and the causal effect of treatment on the surrogate is critical to understanding the value of a surrogate from a clinical perspective. Purpose Traditional regression approaches to determine the proportion of the treatment effect explained by surrogate markers suffer from several shortcomings: they can be unstable and can lie outside the 0-1 range. Furthermore, they do not account for the fact that surrogate measures are obtained post randomization, and thus, the surrogate-outcome relationship may be subject to unmeasured confounding. Methods to avoid these problems are of key importance. Methods Frangakis and Rubin suggested assessing the CE within prerandomization 'principal strata' defined by the counterfactual joint distribution of the surrogate marker under the different treatment arms, with the proportion of the overall outcome CE attributable to subjects for whom the treatment affects the proposed surrogate as the key measure of interest. Li et al. developed this 'principal surrogacy' approach for dichotomous markers and outcomes, utilizing Bayesian methods that accommodated nonidentifiability in the model parameters. Because the surrogate marker is typically observed early, outcome data are often missing. Here, we extend Li et al. to accommodate missing data in the observable final outcome under ignorable and nonignorable settings. We also allow for the possibility that missingness has a counterfactual component, a feature that previous literature has not addressed. Results We apply the proposed methods to a trial of glaucoma control comparing surgery versus medication, where intraocular pressure (IOP) control at 12 months is a surrogate for IOP control at 96 months. We also conduct a series of simulations to consider the impacts of nonignorability, as well as sensitivity to priors and the ability of the decision information criterion (DIC) to choose the correct model when parameters are not fully identified. Limitations Because model parameters cannot be fully identified from data, informative priors can introduce nontrivial bias in moderate sample size settings, while more noninformative priors can yield wide credible intervals. Conclusions Assessing the linkage between CEs of treatment on a surrogate marker and CEs of a treatment on an outcome is important to understanding the value of a marker. These CEs are not fully identifiable; hence, we explore the sensitivity and identifiability aspects of these models and show that relatively weak assumptions can still yield meaningful results.